If \(n=1\) , then the assertion is clear by Corollary REF . Now let \(n>1\) . In view of Proposition REF  and [1]}, \(M\)  is reflexive and so \(M\approx M^{**}\approx \Omega ^2\operatorname{Tr}M^*\) . It follows from Lemma REF  that \(\operatorname{Ext}^{n-1}_R(M,M)\cong \operatorname{Ext}^{n+1}_R(\operatorname{Tr}M^*,M)=0\) . Hence, by [2]}, \(\operatorname{pd}_R(M)<\infty \) .
